Enclosure of the Zero Set of Multivariate Exponential Interval Polynomials

The zero set of one general multivariate exponential polynomial with interval coefficients is enclosed by unions and intersections of closed half-spaces. Tighter enclosures are derived in the bivariate case. Common zeros of polynomial systems can be located by an appropriate intersection of these enclosure sets in an appropriate space. The resulting domains are directly brought into polynomial equation solvers.     

Plasma effects in picosecond-femtosecond UV laser ablation of polymers

Laser ablation of polyimide (PI) and polymethyl-methacrylate (PMMA) at 248 nm with pulse lengths ranging from 200 fs to 200 ps was investigated. The measured ablation rates show minima for pulse lengths of about 5 ps (PMMA) or 50 ps (PI).The reflected fraction of the ablating laser pulse was measured as a function of the pulse length. In the case of PMMA maximum reflectance corresponds to a minimum ablation rate.This behavior can be explained by a dynamic plasma reflection model: A fast build up of a dense plasma is followed by high obscuration for a brief transition time and a self-regulating opacity for the rest of the pulse. This model of plasma mediated ablation leads to a ^1/4-dependence of the ablation rate at fixed fluence, which fits very well to the measured data, in particular if an extension to nanosecond ablation data of PI and PMMA is considered. PACS 52.50.Jm; 61.80.Ba; 42.65.Re     

Abelian and Tauberian theorems for a class of integral transforms

Extending the Wiener-Ganelius method we give Abelian and precise Tauberian remainder results for a class of Fourier kernels which includes the Hankel transform $\text{?(x) = ∫}{}_0{}^{\mathrm{\infty }}\text{√xu J}{}_{\mathrm{r}}\text{(xu) ?(u) du, v ? ?}\text{1}\text{2}$. Further, we discuss applications to Fourier series and integrals.     

Quasi-elastic neutron scattering study of dimethyl-sulfoxide-water mixtures: probing molecular mobility in a nonideal solution

The translational and rotational motions of water and dimethyl sulfoxide, [DMSO, (CH(3))(2)SO] have been investigated using quasi-elastic neutron scattering. Water-DMSO mixtures at five DMSO mole fractions, chi(DMSO), ranging from 0 to 0.75, were measured. Hydrogen-deuterium substitution was used to extract independently the water proton dynamics (d-DMSO-H(2)O), the DMSO methyl proton dynamics (h-DMSO-D(2)O) and to obtain background corrections (d-DMSO-D(2)O). The translational diffusion of water slows down significantly compared to bulk water at all chi(DMSO)>0. The rotational time constant for water exhibits a maximum at chi(DMSO)=0.33 that corresponds to the observed maximum of the viscosity of the mixture. Data for DMSO can be analyzed in terms of a relatively slow tumbling of the molecule about its center-of-mass in conjunction with random translational diffusion. The rotational time constant for this motion exhibits some dependence on chi(DMSO), while the translational diffusion constant shows no clear variation for chi(DMSO)>0. The results presented reinforce the idea that due to the stronger associative nature of DMSO, DMSO-water aggregates are formed over the whole composition range, disturbing the tetrahedral natural arrangement of the water molecules. As a consequence adding DMSO to water causes a drastic slowing down of the dynamics of the water molecule, and vice versa.     

Guiding of intense laser beams in highly ionized plasma columns generated by a fast capillary discharge

We have demonstrated the guiding of laser pulses with peak intensities up to 2.2 x 10(17) W/cm(2) in a 5.5 cm long plasma column containing highly charged Ar ions generated by a fast capillary discharge. A rapid discharge-driven hydrodynamic compression guides progressively lower order modes through a plasma with increasing density and degree of ionization, until the guide collapses on axis. The lowest order mode (FWHM approximately 50 microm) is guided with 75% transmission efficiency shortly before the plasma reaches the conditions for lasing in Ne-like Ar. The subsequent rapid plasma expansion forms a significantly leakier and more absorbent guide.     

Nitrogen‐doped zirconia single crystals

The aim of this work is the preparation of nitrogen‐doped single crystals of cation‐stabilized zirconia. Thin plates of these crystals were nitrided in a graphite heated resistance furnace with nitrogen as reaction gas. Several dwell times and reaction temperatures were tested and their effect on the amount of incorporated nitrogen is investigated. During nitridation at high temperatures a rock salt‐type ‘ZrN’ layer grows on the surface, leading to the destruction of the crystal. In contrast to the fluorite‐type bulk material, which can be described as a fast anion conductor, the surface layer shows electronic conductivity. For possible applications of the bulk material (solid electrolyte) the formation of the surface layer must be avoided. Therefore, the interface between surface epilayer and bulk material was investigated in detail by electron microscopy methods. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)